Aperiodic Monotonic Characteristic Series

GENERA

Monotonic characteristic series of polygonal numbers (starting from 1)

$\displaystyle \sum_{n\geq1} \chi\left(P_r(n)\right) = \dfrac{2r-7}{6}$ (unstable)

$1+\underbrace{0+\cdots+0}_{(r-2) \text{ zeros}}+1+\underbrace{0+\cdots+0}_{2(r-2) \text{ zeros}}+1+\underbrace{0+\cdots+0}_{3(r-2) \text{ zeros}}+1+\cdots = \dfrac{2r-7}{6}$ (unstable)

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